Smullyan on 'not', 'and', 'or', 'if', 'all', 'some (at least one)', and 'the'.
Bartlett defines Grice as a logician -- So is Smullyan. (He was a student of Carnap -- visit the Carnap Corner).
Raymond Smullyan (known as "Ray" -- "I always found the "-mond" otiose")
was brought up in Far Rockaway Peninsula in Queens.
"Rockaway" may be misleading: it's Native American, and variant spellings
include: Requarkie, Rechouwakie, Rechaweygh, Rechquaakie and
Its meaning is unclear or was unclear to the Dutch when they settled
area, and they just kept it for lack of an idea of a better name
his brother told him:
"Today is April Fool's Day, and I will fool you as
you have never been
As Smullyan recalled, he laid in
bed long after the lights were turned out
wondering whether or not I had
really been fooled. Smullyan concluded that
indeed his brother had fooled
him "as he'd never been fooled before" -- by
not fooling him.
was perhaps the first paradox that Smullyan ever encountered.
Smullyan was thirteen years old his family moved from the Peninsula to
Smullyan attended the Theodore Roosevelt School in the
However, Smullyan wanted to learn about groups, rings and fields,
foundations of mathematics and mathematical logic.
Theodore Roosevelt School did not offer, so Smullyan left the
good to study on his own.
A few years of study certainly put him in a
good position to sit the
College Board examinations, which he did and
entered "The Pacific", not the
ocean, but a college in Oregon.
Smullyan moved to Reed, in Oregon (named after E. Abingdon, Mass.-born
Simeon Gannett Reed and his spouse Amanda, née Wood. -- Reed's estate was
left to his spouse, with instructions to use it to assist in the cultural
and intellectual development of Portland. When Mrs. Reed died not much
progress towards the instructions of her spouse. But not long after, the
estate established Reed in Portland. W. M. Ladd (son of Reed's former
partner W. S. Ladd) provided the lands on which Reed stands today, and
all of Reed's estate was passed onto Reed).
Smullyan went south, to San Francisco, and stayed there, but
not for long.
He returned to New York ("where I belonged") where he continued to
logic on his own.
He played chess a lot. One of his friends
said to him, "If *I* were to
compose a chess problem, it would be to deduce
what happened earlier in the
This struck Smullyan as a
fascinating idea, and was his source for his
studies in "retrograde
analysis" -- that looks for a problem which has a unique
solution, yet looks
Later, he enrolled at the University of Wisconsin,
moving after two terms
to Chicago where he began to take courses at the
university but gave up
after only one semester.
He continued to
study on his own.
He then returned to New York where he spent two years.
During these years
he performed in nightclubs in Greenwich Village.
He later returned to Chicago, took various courses at the university
continuing to perform at nightclubs. His patter was especially
(although himself a shy person).
He also worked as a
salesman for a vacuum cleaner company.
One of Smullyan's teachers at the
University of Chicago was Rudolf Carnap
('if you've heard of him, or even
if you haven't', as Geary quips).
Carnap recommended Smullyan for a
mathematics post at Dartmouth, the
liberal arts college in Hanover, New
Hampshire -- named after the earl of
Dartmouth -- i.e. the earl of the
mouth of the river Dart in Devon, England.
Smullyan had no formal
qualifications at this time.
Smullyan taught at Dartmouth while he earned
his B.S. from the University
Smullyan published an
essay, "Languages in which self-reference is
possible" in The Journal of
Symbolic Logic. It is about languages in which
self-reference is possible.
His next essay was "Undecidability and recursive inseparability" which
aimed to prove two results on undecidability.
By the time the second
of these essays appeared, Smullyan was at Princeton
working under Alonzo
Church for his [i.e. Smullyan's, not Church's]
being awarded his Ph.D. from Princeton, he was appointed to a post
at Princeton -- named after some prince [There is no official
backing, but Princeton is considered to be named after Prince William
Orange. My favourite theory is that the name came from a large
Mr. Henry Prince, but I grant a royal prince seems a more 'verifiable'
eponym for the settlement, as three nearby towns had similar names, to wit:
Kingston, Queenstown and Princessville -- and it is hard to derive
"Princesville" from Mr. Henry Prince]
Smullan published several
mathematical essays ('entertaining if you are
into that sort of thing',
Geary editorialises) during this Princeton period.
And essay entitled,
"Exact separation of recursively enumerable sets within
written jointly with Hilary Putnam.
Smullyan also published the essay
"Theories with effectively inseparable
nuclei", to be followed by "Extended
canonical systems", "Elementary formal
systems", and "Monadic elementary
formal systems" -- "Not precisely items of
the New York Times bestselling
list", Geary comments).
Smullyan also published the essay, "Theory of
formal systems" which was
published by Princeton University Press.
Kreisel (whom Witters loved) reviewed the book, and says that it gives
"most elegant exposition of the theory of recursively enumerable sets --
striking improvement over previous expositions."
later appointed to the Yeshiva in New York, and then moved to
(formerly Hunter's Bronx campus, which at the time joined the City
University of New York).
Later he went to Indiana, and took the Oscar
Ewing chair (named after
Greensburg-born O. R. Ewing)
publications include essays on the foundations of mathematics
Usually Smullyan begins with fun-filled monkey tricks
with devilish new twists, spinning a logical labyrinth of
even more complex
and challenging problems as he delves into some of the
deepest paradoxes of
logic and set theory, including Gödel's revolutionary
undecidability. He provides a guided tour of Infinity,
explaining the pioneering
discoveries of Georg Cantor, who was the first to
put the subject on a logically
He also published
"First-order logic", which deals primarily with the
proofs of, and the
interconnections between, various formulations of the
for first-order logic. The book combines elegance with
"A good student should be able to read it almost without a
unless you count the author of the book as a teacher,
He also published "Gödel's incompleteness theorems", which
he wrote "for
the philosopher or any other curious reader who has at least
acquaintance with the symbolism of first-order logic, and who can
logical validity of a few elementary formulas."
essay on incompleteness theorems was the first of a series of texts
appeared in quick succession.
It was followed by "Recursion theory for
"Diagonalization and self-reference" ('the first part
deals with diagonalisation; the
second with self-reference', Geary's review
Smullyan co-authored with Melvin Fitting "Set theory and the
problem" where consistency and independence proofs are given
along with some
charming set pieces on countability and uncountability and
In the classroom, Smullyan is anything
but leisurely or quiet.
Those who watched him teach a logic course,
would see him lurch to the
blackboard (where he writes in a serviceable
hand and in complete sentences)
and paced about his desk, fidgeting and
He occasionally breaks into a small sibilant laugh at
problems that seemed
to leave his students somewhat confused than amused
(as perhaps Smullyan's
laugh would indicate).
One of Smullyan's
hobbies is astronony. He loves observing through his
telescope, and he
ground the six inch mirror himself.